On the first 5 quizzes of his physics class, Omar got an average score of 78. What does he need on the next quiz to have an overall average of 81?
Answer: Let his score on the next quiz be $x$ The sum of all of his scores is then $5 \cdot 78 + x$ The same sum must also be equal to $6 \cdot 81$ Solve: $x = 6 \cdot 81 - 5 \cdot 78 = 96$.